I went to an interesting talk by Ed Southall (author of Yes: But Why?) at Mathsconf. He talked about area of triangle problems, which I thought about again as I was teaching it this week.

In his opinion, we often test the wrong skill. That is, we test that students can multiply and half, but not which lengths to multiply and half. He has a nice worksheet where you just identify the height and the width of various triangles.

I was looking for a worksheet on finding the area of triangles, and was reminded of this and struck by how many simply gave two sides. I was also struck by how much of the extension focused on compound shapes (which in my mind is a different skill), rather than on giving students more information that they needed.

In this worksheet I have tried to design a progression. From counting squares all the way up to giving students information overload and expecting them to pick out what to do.

If I were to add more extension I would include the angles. I think it would lead to interesting discussions.